%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : KLE075+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:46:58 AM UTC 2026
% Result : Theorem 0.14s 5.44s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 24 unt; 0 def)
% Number of atoms : 40 ( 34 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 16 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 11 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(multiplicative_left_identity,axiom,
! [A] : multiplication(one,A) = A,
file('KLE001+0.ax',multiplicative_left_identity) ).
fof(domain2,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('KLE001+5.ax',domain2) ).
fof(goals,conjecture,
! [X0] : domain(multiplication(one,domain(X0))) = domain(X0),
file('theBenchmark.p',goals) ).
fof(f_7_1,plain,
! [A] : multiplication(one,A) = A,
inference(fof_nnf,[status(thm)],[multiplicative_left_identity]) ).
fof(f_7_2,plain,
! [U_11] : multiplication(one,U_11) = U_11,
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
multiplication(one,U_11) = U_11,
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_14_1,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(fof_nnf,[status(thm)],[domain2]) ).
fof(f_14_2,plain,
! [U_28,U_27] : domain(multiplication(U_28,U_27)) = domain(multiplication(U_28,domain(U_27))),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
domain(multiplication(U_28,U_27)) = domain(multiplication(U_28,domain(U_27))),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_18_1,negated_conjecture,
~ ! [X0] : domain(multiplication(one,domain(X0))) = domain(X0),
inference(negate,[status(cth)],[goals]) ).
fof(f_18_2,negated_conjecture,
? [X0] : domain(multiplication(one,domain(X0))) != domain(X0),
inference(fof_nnf,[status(thm)],[f_18_1]) ).
fof(f_18_3,negated_conjecture,
? [U_32] : domain(multiplication(one,domain(U_32))) != domain(U_32),
inference(variable_rename,[status(thm)],[f_18_2]) ).
fof(f_18_4,negated_conjecture,
domain(multiplication(one,domain(sK1))) != domain(sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_32,sK1)],[f_18_3]) ).
fof(f_18_5,negated_conjecture,
domain(multiplication(one,domain(sK1))) != domain(sK1),
inference(definitional_conversion,[status(esa)],[f_18_4]) ).
cnf(f_18_6,negated_conjecture,
domain(multiplication(one,domain(sK1))) != domain(sK1),
inference(clausify,[status(thm)],[f_18_5]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_6,axiom,
( domain(Eq_x_0) = domain(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(t1,plain,
domain(multiplication(one,domain(sK1))) != domain(sK1),
inference(start,[status(thm),parent(0:0)],[f_18_6]) ).
cnf(t2,plain,
( domain(sK1) != domain(multiplication(one,domain(sK1)))
| domain(multiplication(one,domain(sK1))) = domain(sK1) ),
inference(extension,[status(thm),parent(t1:1)],[equality_2]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( domain(multiplication(one,sK1)) != domain(multiplication(one,domain(sK1)))
| domain(sK1) != domain(multiplication(one,sK1))
| domain(sK1) = domain(multiplication(one,domain(sK1))) ),
inference(extension,[status(thm),parent(t2:2)],[equality_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( sK1 != multiplication(one,sK1)
| domain(sK1) = domain(multiplication(one,sK1)) ),
inference(extension,[status(thm),parent(t4:2)],[equality_6]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( multiplication(one,sK1) != sK1
| sK1 = multiplication(one,sK1) ),
inference(extension,[status(thm),parent(t6:2)],[equality_2]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
multiplication(one,sK1) = sK1,
inference(extension,[status(thm),parent(t8:2)],[f_7_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
domain(multiplication(one,sK1)) = domain(multiplication(one,domain(sK1))),
inference(extension,[status(thm),parent(t4:3)],[f_14_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t4:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE075+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.39 % Computer : n017.cluster.edu
% 0.10/5.39 % Model : x86_64 x86_64
% 0.10/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.39 % Memory : 8046.5625MB
% 0.10/5.39 % OS : Linux 6.8.0-71-generic
% 0.10/5.39 % CPULimit : 300
% 0.10/5.39 % WCLimit : 300
% 0.10/5.39 % DateTime : Sat Sep 19 11:45:03 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.14/5.44 % SZS status Theorem for theBenchmark
% 0.14/5.44 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------